Hist. Geo Space Sci., 11, 199–205, 2020 https://doi.org/10.5194/hgss-11-199-2020 © Author(s) 2020. This work is distributed under the Creative Commons Attribution 4.0 License. Carl Friedrich Gauss and the Gauss Society: a brief overview Axel D. Wittmann1, 1Institut für Astrophysik, University of Göttingen, 37124 Rosdorf, Germany retired Correspondence: Axel D. Wittmann ([email protected]) Received: 20 May 2020 – Revised: 24 July 2020 – Accepted: 1 August 2020 – Published: 8 September 2020 Abstract. Carl Friedrich Gauss (1777–1855) was one of the most eminent scientists of all time. He was born in Brunswick, studied in Göttingen, passed his doctoral examination in Helmstedt, and from 1807 until his death, was the director of the Göttingen Astronomical Observatory. As a professor of astronomy, he worked in the fields of astronomy, mathematics, geodesy, and physics, where he made world-famous and lasting contributions. In his honour, and to preserve his memory, the Gauss Society was founded in Göttingen in 1962. The present paper aims to give nonspecialists a brief introduction into the life of Gauss and an introduction into the Gauss Society and its history. 1 Carl Friedrich Gauss – an unusual career in famous because in 1801 he had rediscovered the missing science planet of Ceres Ferdinandea. Gauss was born in Brunswick on 30 April 1777. At the age of about 3 years, Gauss’s tal- Carl Friedrich Gauss was one of the most eminent scien- ents in mathematics became evident, and a bit later, in ele- tists ever, and, like, for example, Archimedes (288–212 BCE) mentary school, he himself discovered a fast algorithm for or Sir Isaac Newton (1642–1727), whom he admired most, finding the sum of an arithmetic series. He was 9 years old was competent and singularly made everlasting contribu- at the time. Subsequently, Gauss was sponsored by Carl Wil- tions in more than one field, namely mathematics, astron- helm Ferdinand, the Duke of Brunswick, and after complet- omy, geodesy, and physics. He was an outstanding genius ing high school, he received a stipend which enabled him to in mathematics, but his main profession (from which he study “abroad”, at the university in Göttingen, which was fa- earned his income) was that of an astronomer. At the age mous for its collection of mathematical literature. This was of 30 years, he became a professor of astronomy and the di- quite unusual because, at that time, Brunswick had a state rector of the Göttingen Observatory. Another world-famous university of its own in nearby Helmstedt. When he was a astronomer, Nicolaus Copernicus (1473–1543), once wrote student in Göttingen in 1796 (and on a short visit to his par- about this field, as follows: “. while it is a property of all ents in Brunswick), Gauss made his first important discov- sciences to distract from leading a depraved life, astronomy ery in mathematics. He found rigorous evidence for the con- can do this to an especially high degree, apart from the in- structibility of the heptadecagon or the 17-gon. This proof – credibly high degree of satisfaction which it provides” (Her- or disproof – had been sought since the time of Euclid, i.e. manowski, 1996). A similar statement was made by Gauss for more than 2000 years. Even a mathematical genius like in 1804: “According to my feelings, practical astronomy – Johannes Kepler had considered the heptadecagon as being right next to the joy of heart and the inspection of truth in impossible to construct. This discovery became the first entry pure mathematics – is the sweetest pleasure which we can in Gauss’s famous “mathematical diary”, in which he briefly have on Earth” (letter to Farkas Bolyai, 25 November 1804). noted most of his discoveries until 1813. It was typical of This shows that, as a post-doctoral fellow, Gauss was al- Gauss not to publish everything without careful considera- ready interested in astronomy. At that time he was in love tion. But his first-ever publication – a note on his discovery with a local woman, looking for a job, and already world- Published by Copernicus Publications. 200 A. D. Wittmann: Carl Friedrich Gauss and the Gauss Society concerning the heptadecagon – was so lacking in detail about how his result was derived, gave no earlier references, and it did not actually present his proof that it would have been immediately rejected by a modern editor. Actually, Gauss’s papers, due to his laxness in his citation of other publica- tions (he tacitly assumed that everyone would know them anyway), would have been rejected by most of today’s peer- review systems. As a student of classical literature and clas- sical languages (in which he was fluent) in Göttingen, Gauss became more and more interested in astronomy and made his first observations of the night sky using a professional telescope (a mural quadrant by John Bird) at the former (the “old”) Göttingen Astronomical Observatory. This was very famous due to the work of Tobias Mayer (1723–1762), whom Gauss always admired greatly. In September 1798 Gauss re- turned to Brunswick and started his doctoral degree, which he received from the Duke of Brunswick’s own university in Helmstedt. In his thesis, Gauss delivered the first rigorous ar- gument for the “fundamental theorem of algebra”. In August 1800, Gauss published a numerical algorithm for calculating the date of Easter. This was his first astronomical publica- tion, and his algorithm is still in use today. In 1801 he pub- lished his main mathematical monograph, the Disquisitiones arithmeticae. Together with Newton’s Philosophiæ Naturalis Principia Mathematica, this work is considered to be one of the great masterpieces of science. Shortly afterwards, an event occurred which made Gauss turn to astronomy forever and which made him world-famous overnight. It had been Figure 1. Carl Friedrich Gauss, painted by Gottlieb Bier- known for a while that there was a gap in the planetary dis- mann (1887). Reproduction by the author from a calendar dated tances between Mars and Jupiter. As Lichtenberg had stated June 1939; this is the first known colour print of a portrait of Gauss. in his lecture: “According to the gap in the arithmetical pro- gression, one has to place an imaginary planet between Mars and Jupiter” (Gamauf, 1814). the terrible shock after the loss of his beloved Johanna, Gauss This planet was desperately searched for by many people mourned intensively and then married again, this time to Wil- since it provided a unique opportunity to become famous helmine Waldeck, a close friend of his deceased wife, and without an academic education (or even any education at they had three more children. At approximately this time, all). On 1 January 1801, the Italian astronomer Giuseppe Pi- Gauss wrote a paper titled Theoria Interpolationis Methodo azzi observed a small, star-like object of an eighth magnitude Nova Tractata, in which, among other things, he developed which, on the following nights, moved among the stars in the the theory of the fast Fourier transform (FFT), which was in same way that a planet or a comet would. But he could not almost the same form as it is used today. Space constraints continue his observation, and the planet was lost. The most do not permit the mention of Gauss’s many other contribu- famous astronomers of the time tried to calculate an orbit in tions to pure and applied mathematics which made him one order to recover the “lost planet”, but they were wrong by of the most outstanding mathematicians of all time. In 1809, about 10 to 15◦, and it was not until Gauss published his cal- Gauss published his most important monograph in astron- culations that Ceres – as the planet was finally named – was omy, the Theoria Motus Corporum Coelestium, which also rediscovered in December 1801 by Franz Xaver von Zach. contained an account of his method of least squares and the In 1805, Gauss married a charming young lady from Gaussian distribution curve. If the Nobel Prize had existed Brunswick, Johanna Osthoff. She was the great love of his in 1809, Gauss might have received it. Of all the academic life but, unfortunately, died 4 years later. In 1807 – shortly lectures Gauss held in Göttingen, 70 % dealt with astron- before Göttingen came under the rule of Jerôme Bonaparte omy, 15 % with mathematics, 9 % with geodesy, and 6 % – Gauss was appointed as a professor of astronomy and with physics; one would not expect such statistics from a the director of the Göttingen University Observatory by the professor of mathematics. Notwithstanding his mathemati- Hanoverian government. The observatory was under still cal talents, Gauss earned his income as an astronomer. Al- construction, slightly to the southeast of Göttingen and just though he did not like lecturing very much, Gauss edu- outside the town wall, and was finished in 1816. Following cated a school of successful astronomers (among them Schu- Hist. Geo Space Sci., 11, 199–205, 2020 https://doi.org/10.5194/hgss-11-199-2020 A. D. Wittmann: Carl Friedrich Gauss and the Gauss Society 201 macher, Encke, Nikolai, Möbius, Gould, and Klinkerfues) and a slightly lesser number of successful mathematicians (among them Riemann, Dedekind, Cantor, von Staudt, and Schering). With some of his pupils Gauss maintained life- long friendships, and his closest friends were Olbers, Schu- macher, Gerling, and Encke. Competent scientists should change their research inter- ests every 10 years during their lives (this is “Fermi’s rec- ommendation”), and Gauss did that. From 1821 until 1824 he conducted and actively participated in the project of land surveying (“triangulation”) in northern Germany, which ex- tended westwards into what is today the Netherlands and eastwards to the former capital of Prussia, the town of Berlin.